Performance Comparison of Tarry and Awerbuch Algorithms

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Presentation transcript:

Performance Comparison of Tarry and Awerbuch Algorithms

Measurements for performance comparison Message Complexity Tarry (2 x no of edges) Awerbuch (4 x no of edges) Time Complexity Awerbuch (4 x no of nodes) – 2

Experiment Setup Arbitrary graphs are generated for performance measurements Characteristics of the generated graph Nodes are randomly generating on a 10x10 graph No of nodes is determined by the formula no of nodes = density x (100/pi) Edge exists between 2 nodes if the distance between them is less than 1 Density is varied from 1 to 10 to increase the number of nodes in the network Program creates several disconnected graphs of which the largest component is selected as input for experiment.

Experiment and analysis How the experiment was conducted Five graphs were generated at each density (varied from 1-10) A run of both algorithms produced values for message and time complexity. Each data point on the graph represents an average of the 5 readings. Entire experiment is repeated for a higher edge to node ratio in the graphs. Resulting graphs support the expected phenomenon. Expected Results For equal node : edge ratio an increase in no of nodes results in better performance for Tarry For higher edge to node ratio an increase in no of nodes results in better performance for Tarry in terms of Message complexity where as Awerbuch performs better in terms of Time complexity.

Results with arbitrary connected network (equal edge : node)

Results with arbitrary connected network (equal edge : node)

Experiment with network of greater connectivity (higher edge : node)

Experiment with network of greater connectivity (higher edge : node)

Conclusion Tarry performs better in terms of message complexity than Awerbuch in all kinds of networks, where as for networks with higher connectivity as the network size increases latter shows better performance for time complexity as compared to Tarry

Message Complexity Time Complexity 1 4 2 16 10 6.8 8 20 12 11.2 14 D DP1 DP2 DP3 DP4 DP5 AVG 1 4 2 16 10 6.8 8 20 12 11.2 14 11.6 22 6 10.0 32 14.4 30 14.0 3 24 90 36.0 60 44 56 68 88 63.2 42 54 74 48.4 124 48.8 248 308 212 112 812 338.4 158 210 166 102 386 204.4 5 64 80 130 71.2 404 300 332 324 408 353.6 266 218 234 290 245.2 58 46 148 164 89.6 376 480 624 616 652 549.6 238 318 410 426 382 354.8 7 50 392 270 196.0 496 1100 668 1036 1140 888.0 306 642 390 502 558 479.6 196 280 330 204.0 552 856 1396 1380 1612 1159.2 350 482 650 690 702 574.8 9 72 304 440 460 309.2 1216 1296 1476 1784 1768 1508 682 670 730 774 798 730.8 140 222 398 476 260.0 808 1432 1600 1828 1428.8 498 766 758 770 870 732.4

Message Complexity Time Complexity A D DP1 DP2 DP3 DP4 DP5 AVG 1 30 34 42 80 52 47.6 2 60 68 84 160 104 95.2 58 62 78 98 82 75.6 54 200 192 219 242 181.4 108 400 384 420 484 359.2 74 194 162 166 206 160.4 3 212 246 282 352 376 293.6 424 492 564 704 752 587.2 270 294 302 270.8 4 488 732 686 820 682.4 976 1464 1372 1640 1364.8 402 410 438 418 434 420.4 5 844 1272 1392 1482 1256 1249.2 1688 2544 2784 2964 2512 2498.4 542 598 602 586 585.2 6 1038 904 1440 1800 2000 1436.4 2076 1808 2880 3600 4000 2872.8 618 574 678 706 714 658 7 1606 1842 1448 1890 1780 1713.2 3212 3684 2896 3780 3560 3426.4 810 838 738 806 766 791.6 8 1466 2166 2030 2582 2792 2207.2 2932 4332 4060 5164 5584 4414.4 802 890 886 942 950 894 9 2066 2712 3040 2720 3544 2816.4 4132 5424 6080 5440 7088 5633 1026 1090 1062 1098 1073.2 10 2814 2272 3562 2940 4472 5628 4544 7124 5880 8944 6424 1186 1030 1218 1102 1242 1155.6